They are both pronounced the same - and different from both an english B and V. I've heard it as making your mouth like you're going to make a B sound, then instead of making a 'plosive' sound, make the V sound with your lips like that.
It also helps to realize that spanish people think we mash up our Vs with Fs, because when we say V, our lips are closer to the F shape their ß sound.
abierto is a past participle; past participles are often paired with the verb 'haber.' the equivalant in english being "I had(have) opened the door," opened being a participle, or the verb plus "ed." Spanish past participles are the verb stem plus "ido" (er) or "ado" (ar). irregular verbs, such as "abrir" often end with "to."
Because that's how the tense is formed. "Abrió" is a conjugated verb form (3rd person singular, Indefinido), whereas "abierto" is the past participle that is used to form compound tenses. The past perfect is formed from the Imperfect form of haber and the past participle. While in English they are often the same, think about a verb like go. It's either "she went" or "she has/had gone". You can't say "She had went".